I like this idea. My only caveat would be to choose a rather plain, unpieced border on the current one, so that you don't risk cutting off any patchwork. In other words, my outer border before the binding would be either be a strip of solid or print, but nothing pieced.
Another idea is, instead of binding, to use the birthing method. That would save a lot of time in the short run . Again, use a very simple border near the outermost seam so you don't have to cut into precious pieced areas.